TSTP Solution File: KRS117+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : KRS117+1 : TPTP v3.4.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:28:03 EDT 2009
% Result : Unsatisfiable 17.9s
% Output : Refutation 17.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 14 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 155 ( 73 ~; 67 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 7 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_6,plain,
! [A,C] :
( ( cd(y_nn_1(A))
| ~ ca_vx3(A) )
& ( rinvf(A,y_nn_1(A))
| ~ ca_vx3(A) )
& ( ca_vx3(A)
| ~ rinvf(A,C)
| ~ cd(C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171784440,plain,
( ca_vx3(A)
| ~ rinvf(A,C)
| ~ cd(C) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
fof(axiom_2,plain,
! [A,B,E] :
( ( ~ rinvr(A,B)
| ca_vx3(B)
| ~ cunsatisfiable(A) )
& ( rinvf(A,y_nn_2(A,B))
| ~ cunsatisfiable(A) )
& ( cd(y_nn_2(A,B))
| ~ cunsatisfiable(A) )
& ( ccxcomp(A)
| ~ cunsatisfiable(A) )
& ( rinvr(A,y_nn_1(A,B))
| ~ rinvf(A,E)
| ~ cd(E)
| ~ ccxcomp(A)
| cunsatisfiable(A) )
& ( ~ ca_vx3(y_nn_1(A,B))
| ~ rinvf(A,E)
| ~ cd(E)
| ~ ccxcomp(A)
| cunsatisfiable(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171688152,plain,
( cd(y_nn_2(A,B))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
fof(axiom_11,plain,
cunsatisfiable(i2003_11_14_17_21_37349),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171855160,plain,
cunsatisfiable(i2003_11_14_17_21_37349),
inference(rewrite,[status(thm)],[axiom_11]),
[] ).
cnf(177120800,plain,
cd(y_nn_2(i2003_11_14_17_21_37349,A)),
inference(resolution,[status(thm)],[171688152,171855160]),
[] ).
cnf(177282944,plain,
( ca_vx3(A)
| ~ rinvf(A,y_nn_2(i2003_11_14_17_21_37349,C)) ),
inference(resolution,[status(thm)],[171784440,177120800]),
[] ).
cnf(171695344,plain,
( rinvf(A,y_nn_2(A,B))
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(177131032,plain,
rinvf(i2003_11_14_17_21_37349,y_nn_2(i2003_11_14_17_21_37349,A)),
inference(resolution,[status(thm)],[171695344,171855160]),
[] ).
cnf(177418240,plain,
ca_vx3(i2003_11_14_17_21_37349),
inference(resolution,[status(thm)],[177282944,177131032]),
[] ).
cnf(171708280,plain,
( ~ rinvr(A,B)
| ca_vx3(B)
| ~ cunsatisfiable(A) ),
inference(rewrite,[status(thm)],[axiom_2]),
[] ).
cnf(177165664,plain,
( ~ rinvr(i2003_11_14_17_21_37349,A)
| ca_vx3(A) ),
inference(resolution,[status(thm)],[171708280,171855160]),
[] ).
fof(axiom_12,plain,
! [A,B] :
( ~ rf(A,B)
| rr(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171860552,plain,
( ~ rf(A,B)
| rr(A,B) ),
inference(rewrite,[status(thm)],[axiom_12]),
[] ).
fof(axiom_9,plain,
! [A,B] :
( ( ~ rinvr(A,B)
| rr(B,A) )
& ( rinvr(A,B)
| ~ rr(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171832560,plain,
( rinvr(A,B)
| ~ rr(B,A) ),
inference(rewrite,[status(thm)],[axiom_9]),
[] ).
cnf(178577504,plain,
( ~ rf(A,B)
| rinvr(B,A) ),
inference(resolution,[status(thm)],[171860552,171832560]),
[] ).
fof(axiom_8,plain,
! [A,B] :
( ( ~ rinvf(A,B)
| rf(B,A) )
& ( rinvf(A,B)
| ~ rf(B,A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171826872,plain,
( ~ rinvf(A,B)
| rf(B,A) ),
inference(rewrite,[status(thm)],[axiom_8]),
[] ).
cnf(171790696,plain,
( rinvf(A,y_nn_1(A))
| ~ ca_vx3(A) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
cnf(178547256,plain,
( rf(y_nn_1(A),A)
| ~ ca_vx3(A) ),
inference(resolution,[status(thm)],[171826872,171790696]),
[] ).
cnf(178852912,plain,
( rinvr(A,y_nn_1(A))
| ~ ca_vx3(A) ),
inference(resolution,[status(thm)],[178577504,178547256]),
[] ).
cnf(180258968,plain,
ca_vx3(y_nn_1(i2003_11_14_17_21_37349)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177418240,177165664,178852912]),
[] ).
cnf(171801144,plain,
( cd(y_nn_1(A))
| ~ ca_vx3(A) ),
inference(rewrite,[status(thm)],[axiom_6]),
[] ).
cnf(180283576,plain,
cd(y_nn_1(y_nn_1(i2003_11_14_17_21_37349))),
inference(resolution,[status(thm)],[180258968,171801144]),
[] ).
fof(axiom_5,plain,
! [A,C] :
( ( cc(A)
| ~ cd(A) )
& ( rf(A,y_nn_1(A))
| ~ cd(A) )
& ( ccxcomp(y_nn_1(A))
| ~ cd(A) )
& ( cd(A)
| ~ rf(A,C)
| ~ ccxcomp(C)
| ~ cc(A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171765872,plain,
( rf(A,y_nn_1(A))
| ~ cd(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(180393944,plain,
rf(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)),y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)))),
inference(resolution,[status(thm)],[180283576,171765872]),
[] ).
fof(axiom_7,plain,
! [A,B,C] :
( ~ cowlthing(A)
| ~ rf(A,B)
| ~ rf(A,C)
| $equal(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
fof(axiom_0,plain,
! [A] :
( cowlthing(A)
& ~ cowlnothing(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171623704,plain,
cowlthing(A),
inference(rewrite,[status(thm)],[axiom_0]),
[] ).
cnf(171809944,plain,
( ~ rf(A,B)
| ~ rf(A,C)
| $equal(C,B) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[axiom_7,171623704]),
[] ).
cnf(180350488,plain,
rf(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)),y_nn_1(i2003_11_14_17_21_37349)),
inference(resolution,[status(thm)],[180258968,178547256]),
[] ).
cnf(195123384,plain,
( ~ rf(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)),A)
| $equal(A,y_nn_1(i2003_11_14_17_21_37349)) ),
inference(resolution,[status(thm)],[171809944,180350488]),
[] ).
fof(cd_substitution_1,plain,
! [B,A] :
( ~ $equal(B,A)
| ~ cd(A)
| cd(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171501584,plain,
( ~ $equal(B,A)
| ~ cd(A)
| cd(B) ),
inference(rewrite,[status(thm)],[cd_substitution_1]),
[] ).
cnf(177446920,plain,
cd(y_nn_1(i2003_11_14_17_21_37349)),
inference(resolution,[status(thm)],[171801144,177418240]),
[] ).
cnf(177517864,plain,
( ~ $equal(A,y_nn_1(i2003_11_14_17_21_37349))
| cd(A) ),
inference(resolution,[status(thm)],[171501584,177446920]),
[] ).
fof(axiom_4,plain,
! [A,C] :
( ( ~ ccxcomp(A)
| ra_px1(A,y0_nn_1(A)) )
& ( ccxcomp(A)
| ~ ra_px1(A,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171738856,plain,
( ~ ccxcomp(A)
| ra_px1(A,y0_nn_1(A)) ),
inference(rewrite,[status(thm)],[axiom_4]),
[] ).
fof(axiom_3,plain,
! [A,B] :
( ( ~ cc(A)
| ~ ra_px1(A,B) )
& ( cc(A)
| ra_px1(A,y(A,B)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),
[] ).
cnf(171722600,plain,
( ~ cc(A)
| ~ ra_px1(A,B) ),
inference(rewrite,[status(thm)],[axiom_3]),
[] ).
cnf(178238160,plain,
( ~ ccxcomp(A)
| ~ cc(A) ),
inference(resolution,[status(thm)],[171738856,171722600]),
[] ).
cnf(171775432,plain,
( cc(A)
| ~ cd(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(178311104,plain,
( ~ ccxcomp(A)
| ~ cd(A) ),
inference(resolution,[status(thm)],[178238160,171775432]),
[] ).
cnf(171758712,plain,
( ccxcomp(y_nn_1(A))
| ~ cd(A) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
cnf(178425688,plain,
( ~ cd(y_nn_1(A))
| ~ cd(A) ),
inference(resolution,[status(thm)],[178311104,171758712]),
[] ).
cnf(180436040,plain,
~ cd(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)))),
inference(resolution,[status(thm)],[180283576,178425688]),
[] ).
cnf(182097248,plain,
~ $equal(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_37349))),y_nn_1(i2003_11_14_17_21_37349)),
inference(resolution,[status(thm)],[177517864,180436040]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[180393944,195123384,182097248]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 18 seconds
% START OF PROOF SEQUENCE
% fof(axiom_6,plain,(((cd(y_nn_1(A))|~ca_vx3(A))&(rinvf(A,y_nn_1(A))|~ca_vx3(A))&(ca_vx3(A)|~rinvf(A,C)|~cd(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171784440,plain,(ca_vx3(A)|~rinvf(A,C)|~cd(C)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% fof(axiom_2,plain,(((~rinvr(A,B)|ca_vx3(B)|~cunsatisfiable(A))&(rinvf(A,y_nn_2(A,B))|~cunsatisfiable(A))&(cd(y_nn_2(A,B))|~cunsatisfiable(A))&(ccxcomp(A)|~cunsatisfiable(A))&(rinvr(A,y_nn_1(A,B))|~rinvf(A,E)|~cd(E)|~ccxcomp(A)|cunsatisfiable(A))&(~ca_vx3(y_nn_1(A,B))|~rinvf(A,E)|~cd(E)|~ccxcomp(A)|cunsatisfiable(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171688152,plain,(cd(y_nn_2(A,B))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% fof(axiom_11,plain,(cunsatisfiable(i2003_11_14_17_21_37349)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171855160,plain,(cunsatisfiable(i2003_11_14_17_21_37349)),inference(rewrite,[status(thm)],[axiom_11]),[]).
%
% cnf(177120800,plain,(cd(y_nn_2(i2003_11_14_17_21_37349,A))),inference(resolution,[status(thm)],[171688152,171855160]),[]).
%
% cnf(177282944,plain,(ca_vx3(A)|~rinvf(A,y_nn_2(i2003_11_14_17_21_37349,C))),inference(resolution,[status(thm)],[171784440,177120800]),[]).
%
% cnf(171695344,plain,(rinvf(A,y_nn_2(A,B))|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(177131032,plain,(rinvf(i2003_11_14_17_21_37349,y_nn_2(i2003_11_14_17_21_37349,A))),inference(resolution,[status(thm)],[171695344,171855160]),[]).
%
% cnf(177418240,plain,(ca_vx3(i2003_11_14_17_21_37349)),inference(resolution,[status(thm)],[177282944,177131032]),[]).
%
% cnf(171708280,plain,(~rinvr(A,B)|ca_vx3(B)|~cunsatisfiable(A)),inference(rewrite,[status(thm)],[axiom_2]),[]).
%
% cnf(177165664,plain,(~rinvr(i2003_11_14_17_21_37349,A)|ca_vx3(A)),inference(resolution,[status(thm)],[171708280,171855160]),[]).
%
% fof(axiom_12,plain,(~rf(A,B)|rr(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171860552,plain,(~rf(A,B)|rr(A,B)),inference(rewrite,[status(thm)],[axiom_12]),[]).
%
% fof(axiom_9,plain,(((~rinvr(A,B)|rr(B,A))&(rinvr(A,B)|~rr(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171832560,plain,(rinvr(A,B)|~rr(B,A)),inference(rewrite,[status(thm)],[axiom_9]),[]).
%
% cnf(178577504,plain,(~rf(A,B)|rinvr(B,A)),inference(resolution,[status(thm)],[171860552,171832560]),[]).
%
% fof(axiom_8,plain,(((~rinvf(A,B)|rf(B,A))&(rinvf(A,B)|~rf(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171826872,plain,(~rinvf(A,B)|rf(B,A)),inference(rewrite,[status(thm)],[axiom_8]),[]).
%
% cnf(171790696,plain,(rinvf(A,y_nn_1(A))|~ca_vx3(A)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% cnf(178547256,plain,(rf(y_nn_1(A),A)|~ca_vx3(A)),inference(resolution,[status(thm)],[171826872,171790696]),[]).
%
% cnf(178852912,plain,(rinvr(A,y_nn_1(A))|~ca_vx3(A)),inference(resolution,[status(thm)],[178577504,178547256]),[]).
%
% cnf(180258968,plain,(ca_vx3(y_nn_1(i2003_11_14_17_21_37349))),inference(forward_subsumption_resolution__resolution,[status(thm)],[177418240,177165664,178852912]),[]).
%
% cnf(171801144,plain,(cd(y_nn_1(A))|~ca_vx3(A)),inference(rewrite,[status(thm)],[axiom_6]),[]).
%
% cnf(180283576,plain,(cd(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)))),inference(resolution,[status(thm)],[180258968,171801144]),[]).
%
% fof(axiom_5,plain,(((cc(A)|~cd(A))&(rf(A,y_nn_1(A))|~cd(A))&(ccxcomp(y_nn_1(A))|~cd(A))&(cd(A)|~rf(A,C)|~ccxcomp(C)|~cc(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171765872,plain,(rf(A,y_nn_1(A))|~cd(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(180393944,plain,(rf(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)),y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_37349))))),inference(resolution,[status(thm)],[180283576,171765872]),[]).
%
% fof(axiom_7,plain,(~cowlthing(A)|~rf(A,B)|~rf(A,C)|$equal(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% fof(axiom_0,plain,((cowlthing(A)&~cowlnothing(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171623704,plain,(cowlthing(A)),inference(rewrite,[status(thm)],[axiom_0]),[]).
%
% cnf(171809944,plain,(~rf(A,B)|~rf(A,C)|$equal(C,B)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[axiom_7,171623704]),[]).
%
% cnf(180350488,plain,(rf(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)),y_nn_1(i2003_11_14_17_21_37349))),inference(resolution,[status(thm)],[180258968,178547256]),[]).
%
% cnf(195123384,plain,(~rf(y_nn_1(y_nn_1(i2003_11_14_17_21_37349)),A)|$equal(A,y_nn_1(i2003_11_14_17_21_37349))),inference(resolution,[status(thm)],[171809944,180350488]),[]).
%
% fof(cd_substitution_1,plain,(~$equal(B,A)|~cd(A)|cd(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171501584,plain,(~$equal(B,A)|~cd(A)|cd(B)),inference(rewrite,[status(thm)],[cd_substitution_1]),[]).
%
% cnf(177446920,plain,(cd(y_nn_1(i2003_11_14_17_21_37349))),inference(resolution,[status(thm)],[171801144,177418240]),[]).
%
% cnf(177517864,plain,(~$equal(A,y_nn_1(i2003_11_14_17_21_37349))|cd(A)),inference(resolution,[status(thm)],[171501584,177446920]),[]).
%
% fof(axiom_4,plain,(((~ccxcomp(A)|ra_px1(A,y0_nn_1(A)))&(ccxcomp(A)|~ra_px1(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171738856,plain,(~ccxcomp(A)|ra_px1(A,y0_nn_1(A))),inference(rewrite,[status(thm)],[axiom_4]),[]).
%
% fof(axiom_3,plain,(((~cc(A)|~ra_px1(A,B))&(cc(A)|ra_px1(A,y(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/KRS/KRS117+1.tptp',unknown),[]).
%
% cnf(171722600,plain,(~cc(A)|~ra_px1(A,B)),inference(rewrite,[status(thm)],[axiom_3]),[]).
%
% cnf(178238160,plain,(~ccxcomp(A)|~cc(A)),inference(resolution,[status(thm)],[171738856,171722600]),[]).
%
% cnf(171775432,plain,(cc(A)|~cd(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(178311104,plain,(~ccxcomp(A)|~cd(A)),inference(resolution,[status(thm)],[178238160,171775432]),[]).
%
% cnf(171758712,plain,(ccxcomp(y_nn_1(A))|~cd(A)),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% cnf(178425688,plain,(~cd(y_nn_1(A))|~cd(A)),inference(resolution,[status(thm)],[178311104,171758712]),[]).
%
% cnf(180436040,plain,(~cd(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_37349))))),inference(resolution,[status(thm)],[180283576,178425688]),[]).
%
% cnf(182097248,plain,(~$equal(y_nn_1(y_nn_1(y_nn_1(i2003_11_14_17_21_37349))),y_nn_1(i2003_11_14_17_21_37349))),inference(resolution,[status(thm)],[177517864,180436040]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[180393944,195123384,182097248]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------